6
Question 1. [26 marks]
A ball of mass m=215g is released from rest at a height 1.50m above the ground. A wind blows,
imparting a constant horizontal force of 0.260N. Ignore wind resistance in the vertical direction.
(a) Draw a free-body diagram for the ball, indicating the forces acting.
(b) Find the resultant acceleration of the ball, expressing your answer in terms of components
along the horizontal and vertical directions (
!
r
i
and
!
r
j
, respectively).
(c) Derive the trajectory of the ball (i.e., vertical position y as a function of horizontal
position x) AND sketch it.
(d) Find the horizontal distance travelled by the ball before impact with the ground AND find
the angle of impact.
(e) Determine the speed of the ball immediately before impact.
Question 2. [28 marks]
An experiment is designed to measure the speed of a bullet. The bullet is to be fired into a wooden
block which is free to move on a horizontal surface, finally compressing a spring. The masses of the
bullet and block are
!
mb
=3.62g and
!
mw
=1.43kg, respectively. The spring is found to conform to
Hooke's law (F=-kx) when it is compressed or stretched up to 14.6cm.
(a) First, the spring constant k has to be determined. It is found that the spring is stretched
8.32cm when the wooden block hangs from it. Use this information to calculate the value of
k.
(b) The bullet is fired into the block, becoming lodged in it, and the combined block+bullet
moves a distance 33.2cm before compressing the spring a maximum of 12.3cm. The
horizontal surface is considered to be frictionless. Giving reasons for your working, find:
(i) the speed of the combined block+bullet immediately before the spring is compressed;
(ii) the initial speed of the bullet.
(c) An additional experiment is set up to test whether or not it was reasonable to ignore the
effects of friction between the block and surface in determination of the speed of the bullet.
The block (with bullet lodged inside) is pushed against the spring, compressing it 10.0cm.
On release, the block travels 66.2cm along the horizontal surface before coming to rest.
mb
mw
k
!
u
